How can I draw an arc with array of points in d3 v4

Question

I wanted to draw an arc from an array of points like this:

var points = [
    [
        51.93326250000001,
        21.4375
    ],
    [
        36.72733749999999,
        40.603550000000002
    ],
    [
        21.527537500000008,
        21.4144
    ]
];

I tried with d3.line(), d3.curveBasis() and d3.curveBundle.beta(1).

var arcPath = d3.line()
    .x(function (d) {
         return d[0];
    })
    .y(function (d) {
         return d[1];
    })
    .curve(d3.curveBasis);
    var arc = node.append('path').attr("d", arcPath(points));

But it is drawing a curved line:

which is not what I am looking for. I would like an arc instead:

I don't understand how to use this:

var arc = d3.arc()
    .innerRadius(180)
    .outerRadius(240)
    .startAngle(0);

with my points.

Answer 1

In order to draw an arc, you need to know the center coordinates of its associated circle and its radius.

In this case, as your arc (part of circle) is defined by the coordinates of 3 points, you need to compute the center of the circle defined by these 3 points:

var points = [
  [
    51.93326250000001,
    21.4375
  ],
  [
    36.72733749999999,
    40.603550000000002
  ],
  [
    21.527537500000008,
    21.4144
  ]
];

function calculateCircleCenter(A, B, C) {

  var yDelta_a = B[1] - A[1];
  var xDelta_a = B[0] - A[0];
  var yDelta_b = C[1] - B[1];
  var xDelta_b = C[0] - B[0];

  var center = [];

  var aSlope = yDelta_a / xDelta_a;
  var bSlope = yDelta_b / xDelta_b;

  center[0] = (aSlope*bSlope*(A[1] - C[1]) + bSlope*(A[0] + B[0]) - aSlope*(B[0]+C[0]) )/(2* (bSlope-aSlope) );
  center[1] = -1*(center[0] - (A[0]+B[0])/2)/aSlope +  (A[1]+B[1])/2;

  return center;
}

function distance(A, B) {
  var a = A[0] - B[0];
  var b = A[1] - B[1];
  return Math.sqrt(a*a + b*b);
}

var center = calculateCircleCenter(points[0], points[1], points[2]);

var radius = distance(points[0], center);

var svg = d3.select("svg").attr("width", 200).attr("height", 200);

// The circle
svg.append("circle")
  .attr("cx", center[0])
  .attr("cy", center[1])
  .attr("r", radius)
  .attr("fill", "white")
  .attr("stroke", "black");

var startAngle = Math.atan2(points[0][1] - center[1], points[0][0] - center[0]) + 0.5 * Math.PI;
var endAngle = Math.atan2(center[1] - points[2][1], center[0] - points[2][0]) + 1.5 * Math.PI;

var arc = d3.arc().innerRadius(radius).outerRadius(radius);

var sector = svg.append("path")
  .attr("fill", "none")
  .attr("stroke-width", 2)
  .attr("stroke", "blue")
  .attr("d", arc({ "startAngle": startAngle, "endAngle": endAngle }))
  .attr("transform", "translate(" + center[0] + "," + center[1] + ")");

// The 3 points:
svg.selectAll("small_circle")
  .data(points)
  .enter().append("circle")
  .attr("cx", function (d) { return d[0]; })
  .attr("cy", function (d) { return d[1]; })
  .attr("r", 2)
  .attr("fill", "red");

<svg></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>

---

Concerning the maths:

You can use whatever method to compute the center of a circle defined by 3 points. Here is used this one.

You can then compute the radius of this circle by computing the distance between this center and one of the three points.

And you will also need to know the start and end angles of the arc, based on the angle between the first point and the circle's center and the angle between the last point and the circle's center. This can be achieved using this formula.

---

Concerning the drawing:

Here is how you can draw an arc with d3.js:

var arc = d3.arc().innerRadius(radius).outerRadius(radius);

var sector = svg.append("path")
 .attr("fill", "none")
 .attr("stroke-width", 2)
 .attr("stroke", "blue")
 .attr("d", arc({ startAngle: 0.5 * Math.PI, endAngle: 1.5 * Math.PI }))
 .attr("transform", "translate(" + center[0] + "," + center[1] + ")");

An arc is defined by its radius. More specifically its innerRadius and outerRadius. In our case it's the same thing.

We then specify the center of the arc by translating the arc:

.attr("transform", "translate(" + center[0] + "," + center[1] + ")");

And we specify the start and end angles of the arc this way:

.attr("d", arc({ "startAngle": startAngle, "endAngle": endAngle }))

where startAngle and endAngle are computed based on first/last points and the center:

var startAngle = Math.atan2(points[0][1] - center[1], points[0][0] - center[0]) + 0.5 * Math.PI;
var endAngle = Math.atan2(center[1] - points[2][1], center[0] - points[2][0]) + 1.5 * Math.PI;